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L2-Stability Of A Class Of Nonlinear-Systems

Sundareshan, MK and Thathachar, MAL (1973) L2-Stability Of A Class Of Nonlinear-Systems. In: Journal of Mathematical Analysis and Applications, 42 (3). pp. 674-683.

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Official URL: http://dx.doi.org/10.1016/0022-247X(73)90171-6


Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Item Type: Journal Article
Publication: Journal of Mathematical Analysis and Applications
Publisher: Elsevier Science
Additional Information: Copyright of this article belongs to Elsevier Science.
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 15 Jul 2010 08:59
Last Modified: 19 Sep 2010 06:10
URI: http://eprints.iisc.ac.in/id/eprint/28771

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